results for au:Muma_M in:stat
Mar 20 2017 stat.ME
A distributed multi-speaker voice activity detection (DM-VAD) method for wireless acoustic sensor networks (WASNs) is proposed. DM-VAD is required in many signal processing applications, e.g. distributed speech enhancement based on multi-channel Wiener filtering, but is non-existent up to date. The proposed method neither requires a fusion center nor prior knowledge about the node positions, microphone array orientations or the number of observed sources. It consists of two steps: (i) distributed source-specific energy signal unmixing (ii) energy signal based voice activity detection. Existing computationally efficient methods to extract source-specific energy signals from the mixed observations, e.g., multiplicative non-negative independent component analysis (MNICA) quickly loose performance with an increasing number of sources, and require a fusion center. To overcome these limitations, we introduce a distributed energy signal unmixing method based on a source-specific node clustering method to locate the nodes around each source. To determine the number of sources that are observed in the WASN, a source enumeration method that uses a Lasso penalized Poisson generalized linear model is developed. Each identified cluster estimates the energy signal of a single (dominant) source by applying a two-component MNICA. The VAD problem is transformed into a clustering task, by extracting features from the energy signals and applying K-means type clustering algorithms. All steps of the proposed method are evaluated using numerical experiments. A VAD accuracy of $> 85 \%$ is achieved for a challenging scenario where 20 nodes observe 7 sources in a simulated reverberant rectangular room.
Jul 06 2016 stat.ME
A new robust and statistically efficient estimator for ARMA models called the bounded influence propagation (BIP) \tau-estimator is proposed. The estimator incorporates an auxiliary model, which prevents the propagation of outliers. Strong consistency and asymptotic normality of the estimator for ARMA models that are driven by independently and identically distributed (iid) innovations with symmetric distributions are established. To analyze the infinitesimal effect of outliers on the estimator, the influence function is derived and computed explicitly for an AR(1) model with additive outliers. To obtain estimates for the AR(p) model, a robust Durbin-Levinson type and a forward-backward algorithm are proposed. An iterative algorithm to robustly obtain ARMA(p,q) parameter estimates is also presented. The problem of finding a robust initialization is addressed, which for orders p+q>2 is a non-trivial matter. Numerical experiments are conducted to compare the finite sample performance of the proposed estimator to existing robust methodologies for different types of outliers both in terms of average and of worst-case performance, as measured by the maximum bias curve. To illustrate the practical applicability of the proposed estimator, a real-data example of outlier cleaning for R-R interval plots derived from electrocardiographic (ECG) data is considered. The proposed estimator is not limited to biomedical applications, but is also useful in any real-world problem whose observations can be modeled as an ARMA process disturbed by outliers or impulsive noise.
Jun 03 2016 stat.ME
Linear inverse problems are ubiquitous. Often the measurements do not follow a Gaussian distribution. Additionally, a model matrix with a large condition number can complicate the problem further by making it ill-posed. In this case, the performance of popular estimators may deteriorate significantly. We have developed a new estimator that is both nearly optimal in the presence of Gaussian errors while being also robust against outliers. Furthermore, it obtains meaningful estimates when the problem is ill-posed through the inclusion of $\ell_1$ and $\ell_2$ regularizations. The computation of our estimate involves minimizing a non-convex objective function. Hence, we are not guaranteed to find the global minimum in a reasonable amount of time. Thus, we propose two algorithms that converge to a good local minimum in a reasonable (and adjustable) amount of time, as an approximation of the global minimum. We also analyze how the introduction of the regularization term affects the statistical properties of our estimator. We confirm high robustness against outliers and asymptotic efficiency for Gaussian distributions by deriving measures of robustness such as the influence function, sensitivity curve, bias, asymptotic variance, and mean square error. We verify the theoretical results using numerical experiments and show that the proposed estimator outperforms recently proposed methods, especially for increasing amounts of outlier contamination. Python code for all of the algorithms are available online in the spirit of reproducible research.